President Donald Trump, shown speaking at the Department of Homeland Security in Washington, Jan. 25, 2017, said on Twitter that he wanted a voter fraud probe to look at "those registered to vote in two states, those who are illegal and even those registered to vote who are dead."

President Donald Trump is calling for a "major" investigation into alleged voter fraud in November's presidential election, reinforcing his belief that millions of undocumented immigrants voted illegally and cost him the popular vote.

Trump announced plans for the probe Wednesday on Twitter. He said it would include "those registered to vote in two states, those who are illegal and even those registered to vote who are dead."

White House spokesman Sean Spicer told reporters the investigation would focus not only on the 2016 presidential election but also on past allegations. "This is about the integrity of our voting system," he said.

WATCH:Spicer: Trump’s Election Fraud Claim a 'Long-standing Belief'

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Spicer did not offer specifics about who would conduct the investigation or when it would begin. But he said investigators would explore irregularities such as outdated voter registration rolls and voters who had moved and were registered in more than one location.

Spicer said more details would be available "as the week goes on."

The issue of possible widespread voter fraud faded not long after Trump won the November election by winning the Electoral College vote. But the new president apparently remains upset about losing the popular vote to Democrat Hillary Clinton.

The voter fraud matter returned to the headlines this week when Spicer reiterated Trump's claim that 3 million to 5 million immigrants had illegally voted for Clinton, who outpolled the president by nearly 3 million votes.

WATCH:Pelosi: Trump’s Voter Fraud Claim is ‘Strange’

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Election officials who analyzed the November 8 vote said there were almost no indications of voter fraud, certainly not on the scale Trump cited.

"We are not aware of any evidence that supports the voter fraud claims made by President Trump, but we are open to learning more about the administration's concerns," said a statement by the National Association of Secretaries of State, which represents 40 U.S. state election officials.

"In the lead-up to the November 2016 election, secretaries of state expressed their confidence in the systemic integrity of our election process as a bipartisan group, and they stand behind that statement today," the association added.

Trump lawyers have stated in writing that evidence of fraud was nonexistent in the November 8 election. In a filing last year against Green Party presidential candidate Jill Stein's attempts to force a recount of votes in Michigan, they concluded, "All evidence suggests the 2016 general election was not tainted by fraud or mistake."

House Speaker Paul Ryan, R-Wis., talks to reporters on Capitol Hill in Washington, Jan. 24, 2017. He told MSNBC television Wednesday that if President Donald Trump believed there was widespread voter fraud in the recent election, "the right thing is to get an investigation to get the facts."

House Speaker Paul Ryan, a Wisconsin Republican, said he didn't believe there was widespread fraud. But he told MSNBC television Wednesday that if Trump believed there was, "the right thing is to get an investigation to get the facts."

But South Carolina Senator Lindsey Graham, one of the Republican presidential contenders Trump defeated during the primaries, urged the president to "knock this off." Graham said Trump "needs to disclose why he believes" the election was marred by fraud.

FILE - Sen. Lindsey Graham, R-S.C., shown speaking with reporters in the Senate Press Gallery in Washington, Nov. 15, 2016, says President Donald Trump "needs to disclose why he believes" there was widespread voter fraud in the November election.

Senator Bernie Sanders, a Vermont independent who lost the Democratic presidential nomination to Clinton, told reporters Trump's voter fraud claims were "nonsensical" and "delusional." He said he feared Trump's claims were aimed at paving the way for more restrictive voting laws.

"What I fear about that statement, and that is something we should all worry about ... he is sending a message to every Republican governor in this country to go forward with voter suppression," Sanders said, adding that he thought voter suppression was the greatest democratic crisis facing the United States.

The investigation into voter fraud could be led by the Justice Department, which enforces voting rights laws. But the nation's top law enforcement agency analyzes cases based on whether they can be prosecuted, and it has not become involved in efforts to improve voting systems.

Although Justice Department probes into voter fraud are rare, that department conducted a five-year investigation during the George W. Bush administration. No evidence of fraud was found, and the probe prompted more investigations and forced resignations of then-Attorney General Alberto Gonzales and seven U.S. attorneys.

Any Justice Department probe could be led by Senator Jeff Sessions, the president's choice for attorney general. Sessions has claimed in the past that voter fraud exists, but recently tried to separate himself from Trump's assertion that millions were responsible.

Spicer cited Tuesday a 2008 Pew Research study that supposedly determined that 14 percent of U.S. voters were not citizens. Pew did not produce such a study, but The Washington Post released a disputed 2014 report that came to a similar conclusion.

Pew produced a 2012 study that found evidence of outdated voter registration forms but did not conclude there was actual fraud.